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On the Atkin $ U_t$-operator for $ \Gamma_0(t)$-invariant Drinfeld cusp forms


Authors: Andrea Bandini and Maria Valentino
Journal: Proc. Amer. Math. Soc. 147 (2019), 4171-4187
MSC (2010): Primary 11F52, 11F25; Secondary 20E08
DOI: https://doi.org/10.1090/proc/14491
Published electronically: June 27, 2019
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Abstract: We study the Atkin $ U_t$ operator for Drinfeld cusp forms. In particular, we define newforms and oldforms of level $ \Gamma _0(t)$ and we study basic properties of their slopes. Moreover, we find an explicit formula for the matrix associated to the action of $ U_t$ on $ \Gamma _1(t)$-invariant cusp forms using Teitelbaum's interpretation as harmonic cocycles.


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Additional Information

Andrea Bandini
Affiliation: Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy
Email: andrea.bandini@unipi.it

Maria Valentino
Affiliation: Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università degli Studi di Parma, Parco Area delle Scienze, 53/A, 43124 Parma, Italy
Email: maria.valentino@unipr.it

DOI: https://doi.org/10.1090/proc/14491
Received by editor(s): July 4, 2018
Received by editor(s) in revised form: October 12, 2018, October 26, 2018, and November 29, 2018
Published electronically: June 27, 2019
Additional Notes: While this article was being written, the second author was supported first by an Outgoing Marie-Curie fellowship of INdAM and then by an “Ing. G. Schirillo” fellowship of INdAM
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2019 American Mathematical Society